I saw this in http://www.space.com/12928-falling-satellite-crash-late-september-nasa.html" [Broken] about the debris from the UARS satellite.

This seems like an extremely large probability to me. They do not make any reference on how they computed this. Does anyone here know how they could have come up with this probability?

I would intuitively expect it to be much smaller. I mean 1 in 3200 that a piece of satellite will literally hit someone on earth? That is actually way more likely than I would imagine.

I think they mean the odds of debris hitting any 1 of the nearly 7 billion people on earth. The odds of hitting a specific persion would be 1 / (3200 x 7 billion).

No it doesn't. It means there is a 3199/3200 chance that nobody will be hit, and a 1/3200 chance that at least 1 person will be hit. It's hard to guess how the probability would split between "exactly one person hit" and "more than one person hit", because the distribution of people over the surface of the earth is very far from uniform, and we don't know how much surface area a single impact would affect.

If you think that seems like a "high" probability, remember that it means that if 3200 similar satellites broke up, you would expect some debris to hit a person approximately once. If that was one satellite breaking up every week, you might hit somebody once every 60 years on average.

Let's assume everyone on earth lays flat on the ground, and that avg height is 1.7m and avg width is .45 meters. So each person is 7.65e-7 km^{2}. This multiplied by 6.96 billion people is 5324 km^{2}. The surface area of the earth is 510,072,000 km^{2}. So the fraction of the earth covered by lying down people would be 1.044e-5.

The article says 26 pieces will survive reentry. I guess each piece has a 1.044e-5 chance of hitting a person (assuming the worst case of everyone lying down). If they are scattered and independent of each other, then I would think it's 26*1044e-5 = 2.7144e-004.

Hmmm... 1/3200 = 3.1250e-004, so it is actually sort of close to my number (mine is 1/3684).

I guess it's not really that high after all. Did I do this right, more or less?

I bet they have some sense of where it will fall though, so they aren't necessarily looking at the whole earth. Perhaps they have an area that represents the probably point of impact (much like a hurricane path, for example) and it happens to contain some population center(s). They could certainly get a much higher than expected probability in this case.

Additionally, your area case is much too simplified. Each piece will impact an area, not a single point, so it makes it more likely to hit a person. It also passes through a volume, so it could hit things all along that path. Of course, people don't usually lay down on the ground or stand still, so then you start lessening the chances again.

Suffice it to say that they likely know an area of probability of impact and that they have some model for how likely it is to hit a person should it impact the land portion of that area of probability.

What is the best way to dispose a satellite? A year or two ago, China decided to retire an old satellite by shooting it with a missile. Maybe it was political show off / weapon test masqueraded as a civil purpose.

In terms of danger to Earth population (hit by debris, radioactive waste, etc.), is shooting a satellite more or less dangerous?

Shooting a satellite is a terrible way of getting rid of it, as it just causes more debris to orbit the earth.

Debris in space is a hazard to satellites. If you get enough debris up there, you could create a domino effect where debris strikes a satellite and makes more debris, which in turn strikes another satellite and makes even more debris.

Interestingly, the International Space Station has had to perform emergency maneuvers in order to avoid debris. Also, not too long ago a Russian and an American satellite have collided in space.